Victory in one try
Since there are 2,315 possible target words in Wordle, the probability that you will guess the target in exactly one try is 1/2315 = 0.000432. In fact, it doesn’t matter which of the 2,315 words in the dictionary you choose to use as your initial guess since the probability of success is always 1/2315.
Victory in two tries
The situation is more complicated if your goal is to guess the target within two tries. Let us suppose that you choose “trace” as your first guess. Depending on the target word, Wordle will return one of the 243 patterns (as described in Figure 3 of Letter Frequency and Patterns). For example, if the target word is “dance”, “lance” or “sauce”, then Wordle will return the pattern “**YGG”. These are the only three possible target words that can match this pattern.
If “**YGG” is returned, then your optimum strategy, assuming that your goal is to guess the target within two tries, is to choose “dance”, “lance” or “sauce” as your second guess. It doesn’t matter which of these three words you choose, your probability of success is 1/3.
Note too that not all patterns are possible. E.g. Wordle will never return a pattern of “*YYGY”, no matter what the target word is when you choose “trace” as your first guess.
Figure 1 displays a list of possible patterns after a choice of “trace” as your first guess.
Figure 1 – Patterns after “trace”
Non-zero patterns
For each of the 243 patterns, Figure 1 shows how many targets will match that pattern after an initial guess of “trace”. The figure also lists one of the possible targets that match that pattern (actually the first such target in alphabetical order).
For example, if Wordle returns a pattern of “*****” (i.e. no matches), then we see from the figure that there are 246 possible target words that match that pattern. If this is indeed the pattern that Wordle returns, then you have a 1/246 chance of picking the correct target on the second try (e.g. by choosing the word shown in Figure 1 for that pattern). Also, note that the probability that Wordle returns this pattern after an initial guess of “trace” is 246/2315 (246 targets out of the 2,315 possible targets).
Probability calculation
Using the Law of Total Probability, the probability of guessing the target within two tries is equal to
This is a sum of 243 terms (one per pattern), although terms with no matching pattern are omitted. This leaves 150 terms (93 of the patterns shown in Figure 3 of Letter Frequency and Patterns have no matching targets). Cancelling out terms, the above sum is equivalent to
Thus, the probability turns out to be the number of non-zero patterns for “trace” divided by 2315, which is 6.4795%.
Best initial guess
It also turns out that using an initial guess of “trace” has the best probability of discovering the target within two tries. The next best initial guesses from the basic Wordle dictionary are shown in Figure 2.
Figure 2 – Best initial guesses
In Letter Frequency and Patterns, we suggest that picking guesses with more commonly used letters might be a good strategy (see Figures 1 and 2 of Letter Frequency and Patterns). Figure 2 suggests that picking guesses that maximize the number of non-zero patterns might also be a good strategy. Note that some words (slate, crate, and trace) appear in both lists.
Using the full dictionary
We could also use as our first guess words from the full, 12,497-word dictionary that are not in the basic dictionary. There are 23 such words that are at least as good as the words in Figure 2 (in terms of the probability of winning the game in 2 guesses). The best such words are “salet” (148), “reast” (147), “carte” (146), “caret” (145), “peart” (145), and “carle” (144). The downside of these words is that there is no chance of guessing the target word in one try.
Click here for more information about using the full dictionary.
Download Tables
Click here to download the Excel workbook with the tables in Figures 1 and 2.
Reference
New York Times (2022) Wordle
https://www.nytimes.com/games/wordle/
RS,
I typically use the solution to the previous day’s puzzle as my first guess. Aside from a zero probability first guess, are there any other insights to pull from this approach?
I don’t like the idea of using a predetermined efficient word every day and the idea of choosing one word randomly is kinda gross too.
Hi Tim,
It’s an interesting question. Clearly it reduces you expected score since you abandon the possibility of winning in one try, but this is not a big chance anyway. It does seem that your first guess will almost never be optimal even for subsequent guesses, but I don’t know how big a deal this will be.
Charles
I keep reading that there are only 2315 words in the Wordle dictionary and that Wordle does not repeat answers. Does that mean that after a little over 6 years (2315/365.25) all the available words will have been used? As that day approaches, will the list become so short that the game will become meaningless?
Hi Will,
I imagine that the NY Times will change its policy and add words and/or start to repeat words. I thought that they already took some steps in this direction but I am not sure.
The game is popular and I would imagine that the Times wants people to continue to play it.
Charles
Hello, all-
I’m a strategic pattern thinker but I’m not as strong working with pure probabilities. I’ve been playing Wordle for a month.
I’ve settled on TALON for my first word, because I want to avoid unnecessarily guessing letters that often appear together. For example, A and O are often the middle letter of a __vowel-consonant-E pattern. I’m wasting a guess by including E in my first word.
Similarly, I don’t want to guess E/R or S/T together in my first word.
Thoughts?
Hello Ross,
TALON seems like a perfectly good first guess. As the webpage shows there are better first guesses, but TALON seems to be quite reasonable. My guess is that it suffers by not containing an E.
Charles
Hi Charles,
Earlier you said, “Do you any evidence in favor of this (elimination) strategy?”.
After a bit of programming, yes… I have evidence/proof.
If you accept the premise that the best starting valid wordle will produce the most green tiles and thereby increase the chances to win in 2 tries… then counting the future green tiles produced was easy with this formula…
=IF(E9=””,””,IF(MID(E9,1,1)=MID(TestWordle,1,1),1,0)+IF(MID(E9,2,1)=MID(TestWordle,2,1),1,0)+IF(MID(E9,3,1)=MID(TestWordle,3,1),1,0)+IF(MID(E9,4,1)=MID(TestWordle,4,1),1,0)+IF(MID(E9,5,1)=MID(TestWordle,5,1),1,0))
This will return the number of green tiles per word and then simply get a sum of the all those cells to get a count of future green tiles.
If you put SAUCY in the TestWordle cell, then number of green tiles eventually produced by SAUCY is 796 as of today. SAUCY is currently the best word for trying to win in 2… but SANER is the saner choice and is in the #2 spot. It will produce 786 green tiles giving a good chance for win in 2… but also is better at general word elimination.
With today’s wordle, SANER returned A and E green tiles and thereby eliminated all but 8 words. At that point I had a 1 in 8 chance of winning in two. Of those 8, I picked the word that has the most potential to eliminate other valid Wordles after the next try.
The Wordle I chose did not win, but it eliminated all but one choice for the 3rd try.
BTW, TRACE is not a valid Wordle Word… it was previously used.
If you or anyone would like to know how many future green tiles your word will produce… just send the word and I will return your results.
Ronny,
Thanks for sharing your observations.
Charles
Juice
Hi Charles,
I would like to thank you for posting your statistics and ideas.
However, your premise is completely flawed because you don’t take into account the Wordle words already used in the past. The chance of winning on the first try tomorrow is one in 1281 of the remaining available words. And the chances increase every day. This reduction of the by the available words carries only subsequent guesses.
IMHO, your best starting word selection is also flawed… the words should be ranked by how many words they eliminate… I have found three different ways to do this. And this ranking will also change as the available word list reduces in size.
ALL,
I created a Winning Wordle group on Whatapp for those who would like to discuss strategies for improving your odds at winning Wordle in fewer guesses.
Please join with me if this is of interest to you…
https://chat.whatsapp.com/KamKvtDxyH29ILvbll9ZxB
Hi Ronny,
You are completely correct. I have not taken into account words that have already been used on previous days.
I think ranking potential initial guesses by the number of target words that they eliminate is not necessarily the best strategy. Do you any evidence in favor of this strategy?
Charles
Hi Charles,
My goal is to get my average guesses as low as possible. My current average is 3.3. With some recent improvements in my algorithms, this average is slowly getting lower.
I came here to see if I could get some ideas to increase the “win in 2 tries”.
The starting word that I am using currently is “SANER”. I picked it because
1) it is a valid word,
2) Has no characters that are used twice.
3) It has both a very high character and word elimination weight.
4) With the very high character weight, I believe will likely produce the most green tiles, but my sample data is not yet enough to prove this out. I have made the assumption that more green tiles in the first try will lead to more “win in 2 tries”
5) I have a spreadsheet that I have programmed to help select words and would be willing to share it. It is not user friendly.
Here are my wins using SANER…
FROND 3
SERUM 3
PLAIT 3
WRIST 3
FINCH 4
VOILA 4
BREED 4
MERGE 3
BROTH 3
LOUSE 2
WHINY 4
STEEL 3
BLIMP 3
EQUIP 3
SHANK 3
TITHE 3
Top 10 Starting Wordles
Valid WW Elimination by
Word Char Mix
guess 2220 797 50.0%
RAISE 2220 690 2565.00
SANER 2165 788 2559.00
ARISE 2220 666 2553.00
STARE 2195 687 2538.50
AROSE 2212 643 2533.50
LATER 2183 605 2485.50
ALERT 2183 462 2414.00
SHARE 2047 718 2406.00
AISLE 2132 539 2401.50
SPARE 2050 684 2392.00
I removed words with duplicate letters as 2nd try elimination words… this seems to have improved results.
Doing that mix elimination seems to have improved results. I am still tweaking it because I have only used it a few days. I will continue to find a better way to mix them.
That maths is so cool!
I have played Three times this year.
I st time I got in in three
2nd time I got it in 2
3rd time I got it in 2.
I’ve played less than ten times in my life.
Am I a computer? Autistic? Or both? I don’t know how I could have done that.
I used the word GREAT….
Hi Sue,
I agree that you are “Sue the Great”. You beat the odds and seem to have had fun in the process. That is indeed GREAT.
Charles
To each their own, but it seems silly to me to develop a strategy to try to increase your chances of solving in two tries, which is going to happen such a small percentage of the time anyway, and is very highly dependent on sheer luck. It seems to me that the strategy of the most skillful players involves trying to solve in the lowest number of turns, on average, over the long-term. This strategy, in fact, will reduce the number of times a player with solve in exactly two tries. I say this, because efficient solving in most cases requires using optimal elimination words in round two, and those words rarely double as possible solutions. Some players do not want to “waste” a guess in round two, and throw away that very small chance of solving, even though a word like tha will almost always result in not winnowing the remaining possible solutions efficiently, which, in the long-term, will increase your number of turns to solve average.
Hello David,
I agree with you. Often the strategy for winning in two guesses undermines your ability to win in the fewest number of guesses.
Actually, trying to win in two guesses was instrumental in my understanding how to win in the lowest number of steps. After analyzing winning in two guesses, I focused on winning in three guesses, and from there in the fewest number of guesses.
Charles
Hi Charles,
I’ve got a nine game streak of solving Wordle in two guesses, from puzzle #976 to #984. I solved puzzle #975 in one guess. Haven’t tried today’s yet. What are the odds? My friends find my streak hard to believe and it’s starting to freak me out a bit.
Will,
This is extremely rare. The probability for any 10 game sequence is at most (1/2315) x (149/2315) ^ 9 = 0.000000000000008.
If you have been keeping track of previous target words, then you can probably lower the odds somewhat (assuming that the approach that the NY Times uses hasn’t changed).
Charles
Hello Charles, This is a very thoughtful and engaging website. Thank you!
I have played Wordle 548 times. My success rate is the following:
1 – 0, 2 – 23, 3 – 141, 4 – 231, 5 – 120, 6 – 26, Fail – 5. This seems like a decent enough result, but nothing special, especially compared to folks who are more mathematically tactical in their approach. Yet, according to the game, my “skill” score tends to be between 88 – 94, it is frequently above 96 and yet rarely below 85. Even when my “skill” score is over 96 I am often shocked by how many folks complete in fewer guesses. On certain days when the target is a more unusual word I often notice that there is usually (just my sample) between 1.2% and 3.4% who get the answer on the 2d guess, even though it is a fairly obscure word with an odd letter pattern, like today, Wordle No. 956. In observing this over and over again my unscientific conclusion is that maybe 1.5 – 2.0% of total Wordle games may typically have cheating. Perhaps they have have a second browser where they play covertly? Can you statistically estimate what % of Wordle games are likely played by a cheater? Thanks!
Hi Robert,
1. Your scores seem pretty good to me. To avoid winning in 6 or losing you probably need to avoid getting into situations where there are several possible words with a similar pattern and so each guess doesn’t give you any further information and so all you can do is guess again and hope.
2. As you can see from this webpage, if a person uses the optimal strategy they have a 6.8% chance of winning within two tries. This would mean that 6.8% of the players would win in 1 or 2 tries, which is higher than 1.2-3.4%. Thus, 1.2-3.4% is possible. That the word is obscure shouldn’t reduce the odds by much
3. I suspect that there is some cheating going on, but that shoudn’t prevent most people from enjoying the game. How to estimate the percentage who are cheating is difficult. This would require gathering a sample of results and analyzing them statistically. I don’t have a “silver bullet” for ding this.
Charles
Great website! Love the stats and comments from fellow Wordle addicts.
A quick check, how would you calculate the odds of 2 correct second-guess solutions on 4 consecutive days? 0.065^4?
Hi Christo,
Glad you like the site.
Yes, 0.065^4 is the probability of correct guesses in 1 or 2 tries on 4 consective days.
Charles
I got Wordle 2 tries, in hard mode, without cheating, 4 times in the last 7 days. Yes, I know I was VERY lucky. I just don’t know exsctly how lucky. Can you tell me the odds?
Hi Mike,
The probability of this occurring is 0.0505%. This can be calculated in Excel by the formula =BINOM.DIST(4,7,150/2315,FALSE).
Charles
Hi Charles,
Can’t say I fully understand the math but tried your Excel formula and got the same results, roughly 1 chance in 2000. Those are pretty slim odds but not as slim as I thought they might be.
Thanks & Regards, Mike
Hi Mike,
I am also a bit surpised that the odds weren’t even longer. In any case, congratulations on getting such good results.
One last observation. These results are based on an initial guess of TRACE. If you choose a different first guess the odds may be worse.
Charles
So, this would be the odds of picking one single seven day window, and calculating the odds of someone getting four deuces in that window? Of course, if somebody has been playing for 900 games, there are 893 of those windows, So, if the question were phrased a little differently, such as what the odds are of somebody getting for deuces at some point within a seven day window, that number would be quite a bit higher. I know that’s not the question that was asked, but it just illustrates that if the universe of events is factored in, the problem can be looked at a bit differently.
A friend in our Wordle group had 6 2’s in October, 9 2’s and 2 1’s in November and, as of today December 21st, 10 2’s in December. The rest of us suspect cheating. What are the odds?
Dave.
Hi Chris,
The probability of getting 25 2’s and 2 1’s in 82 games is at most .00000000000000038249. This means that if 38,249,000,000,000,000 people played these 82 games, on average one of them would achieve this result. This is a very low probability indeed.
My answer assumes that knowledge about the results of prior games isn’t useful. If the target word can’t be repeated and your friend has been keeping good records of prior target words, then the odds will be better, but still very low.
Charles
The NYT Wordle Bot will analyze your game, compare it to the average player, and point out any bad moves you made. It’s very helpful, and I think it’s improved my play considerably.
One of the things it does is report statistics on the most common first words (ADIEU is most popular, although far from most effective), and the most common second guesses, third guesses, etc. for each game. What I’ve noticed is that the most common second guess is the correct answer – every single time. (We’re talking 100% of the games played so far.) I suspect that a lot of bogus games (where the player knows the answer in advance) are involved in producing this rate of second-guess solutions, but was wondering what the actual odds were.
“ What I’ve noticed is that the most common second guess is the correct answer – every single time. ”
That hasn’t been my experience, and in fact, I just checked the results of my game today, and that was NOT the case. Wordle 976, solution was Match. My opener was TARSE, followed by Pitch. But Paint, Patch, and Baton were the top three most popular guesses in that scenario in round two, Match came in 4th.
I guess I can see that with Many possible solutions, remaining, and most players not being sophisticated enough players to come up with the bots top choices on their own, the guesses are going to be distributed all over the place. So if people are cheating and jumping to the answer on round two, the solution word is probably going to be overrepresented compared with what probability calculations might estimate
Thing is, it’s not strictly about the odds. I mean, the elimination of letters and the combination of letters such as the likelihood of ST being together or TH being together or QU when U is the only vowel left to pick for random examples are intuitively known to English speakers.
Quite true. The patterns and rules of English spelling, and some of Wordle’s rules (e.g., no plurals) are what make the better Wordle-solving computer algorithms so complex.
FWIW, the NYT Wordle Bot usually repeats any yellow letters, in different positions, on the second guess, and I now use this strategy. The odds of nailing a green this way are pretty good – much better than when using five completely new letters.
Actually, I wouldn’t say the bot “usually” employs this strategy. I have seen it do it every once in a while, But not for the vast majority of cases. In fact, I’ve seen a surprising percentage of the time where the bot chooses to not play the yellow letter AT ALL, in favor of introducing new letters instead. The problem is, with the remaining solution sets being relatively large in many cases, it is really hard for a human learn from all these scenarios as to when it is advantageous to play the yellow letter twice, versus once in a different position, versus not using it at all. If you write down the bot’s choice for round two after a specific scenario in round one, you can certainly just reuse that word if that same scenario comes up again. But, in later rounds, the odds of you encountering the exact same scenario in the future are extremely lowered, so it would probably be too cumbersome to try to record the bots choices for round three guesses, based on all the possible scenarios you may have encountered after rounds one and two combined,.
Hoping you can give me some idea of the probability of some stats that a friend of mine has given me. In 530 games played, he has 6 ones and 73 twos. Using an online probability calculator, I came up with something like a 1 in 2,777,777 chance of getting 6 ones, but am rather unsure of the math as the result was written as 3.597 x 10 to the -7th power. I’m hoping you can tell me if my calculation is correct and what the probability of them getting 73 twos is. Thank you.
Don,
The probability of winning in one in one game is 1/2315.
The probability of 6 such ones in 530 games can be calculated in Excel via the formula =BINOM.DIST(6,530,1/2315,False), which returns the value 1.5501E-07. This is scientific notation for 1.5501 x ten raised to the -7 power. This is equivalent to .00000015501. This is equivalent to one chance in 6,451,209.
If you consider the case of getting 6 or more ones, then the probability rises to .00000016017, i.e. one chance in 6,243,385.
Keep in mind, that although it is not so likely that any one person will get 6 or more ones in 530 games, if millions of people play Wordle, it is likely that someone will get 6 or more ones in 530 games. This is similar to the situation in playing the lottery.
Charles
Don,
One more thing. The calculations I made assume that you don’t have any memory of the previous day’s winning word. If you do, then the probability of winning in one improves from 1/2315 on day 1 to 1/1786 on day 530. This will increase the chances of getting 6 ones in 530 games.
Charles
Wordle (so far) doesn’t repeat words. Given the 1st guess word list you posted, you have to go all the way down to TRIED before finding a non-S containing word that hasn’t;t already been used. I want my 1!!!!
https://www.rockpapershotgun.com/wordle-past-answers
I don’t like S words because Wordle doesn’t use plural four-letter words. But mathematically, if you accounted for this, PARSE is the highest probability non-used word remaining.
Regarding WORDLE stats….When the puzzle is not done one day, is it ignored in the stats (other than breaking a streak) or is it counted as a loss?
Hi Pam,
Which stats are you referring to?
Charles
The Wordle stats….games played, win %STATISTICS etc
Number of games played, 409
Win percentage, 98
Current Streak count, 19
Max Streak count, 82
GUESS DISTRIBUTION
1
0
2
11
3
80
4
171
5
108
6
29
Today (sunday 8-20) I did what I often do and started with a 5 letter word that relates to my day or that I happen to see where ever I am playing. We had friends over for dinner so guest came to mind. I think I might have hollared when I saw 4 green squares with only the first letter grey. I got a rare (for me) 2 with “QUEST”. Totally luck!
It looks like Pam’s question was never answered. Wordle does not factor a non-played game into the bar graph histogram, so it doesn’t treat it like a loss, but it does restart the streak to zero. I think this is because they are thinking that people might decide to abandon a game round four or five if they think they’re probably going to lose, just so they can keep their streak alive.
Hi Charles,
My brother’s current sequence is 32332233.
Is this as suspicious as it looks?
Many thanks,
Bob
Hi Bob,
Best case the probability of getting 1 or 2 is about 6.48% best case. The probability of 1, 2, or 3 is about 60.0% best case, but the strategy for achieving this reduces the probability of getting 1 or 2. Even if we ignore this fact, the probability of getting 3 2’s and 5 3’s in 8 games is about 0.067% best case. The probability of guessing within 3 tries in 8 games is 1.67%, but the probability of guessing within 3 tries in 8 games where at least 3 tries are 1 or 2 tries is 0.078%. Thus, 32332233 is rare but possible.
Charles
Since many of the questions here are of the form “My friend/nemesis won a series of games with a surprisingly good score. Are they cheating?” I’ll remind people that given the huge numbers of people playing, even score sequences that are million to one longshots, and therefore highly suspicious, are achieved by hundreds of honest players all the time.
So while the chances of one particular person’s particular friend scoring so well is exceedingly rare. The chances of someone’s particular friend/nemesis scoring so well is exceedingly common. So, getting a great score and telling some friends who become suspicious, look it up online and report their suspicions here, is not proof of cheating at all.
I agree with this assessment, and I think this concept is one that can be difficult for many to grasp when looking at probabilities. For example, if someone asks “what are the odds of somebody getting two deuces within a seven day span?” the answer would be a lot different if you are talking about one specific seven day span, versus considering the entire universe of Wordle games. If Someone has played 900 games, there are 893 seven game windows, so the odds of somebody getting two deuces within any of those windows is certainly much higher than just picking only one of those windows.
I figured out, using the word, “Learn” gives me the best chance. I got the Wordle today in 2 tries. I had 4 letters in my first try. I can usually get it in 2 tries or maybe, 3 tries , zero help! I had witnesses today at work and were amazed I got it in 2 tries.
“ I can usually get it in 2 tries or maybe, 3 tries , zero help!”
I call FLAT OUT BS on this claim. It is absolutely not supported by the mathematics of this game. Even if you picked the very best start word out there, you are probably going to average having at least 40 possible solutions remaining after round one. Some games, you may have only a handful of possibilities, sometimes more than 100. So, to get a deuce even 25% of the time, you’d probably have to have your opening word result in having only four remaining solutions every single day. That’s obviously not going to happen. Even in that scenario, you’re not even going to solve in three turns half the time, so your claim is preposterous on its face. I don’t know why so many people feel the need to lie about their game on the Internet, but it’s pretty rampant.
This isnt true. The words are not known. There are more 5 letter words than those used in Wordle.
Hi Tim,
I believe that this was true until fairly recently. I plan to update the Wordle portion of the website shortly to reflect some newer information.
Charles
of course, but undoubtedly due to the lack of plurals, -ed and -er endings. I also suspect the game avoids words that have 5 or more starting letter possibilities, eg _ATCH [where B C H L M N P and W could all fit], and -ing words…
Not exactly, Dick. Several months ago, I was feeling lucky after starting with LATCH, WTH a return PATTERN of *GGGG. Imagine my dejection after using M, W, B, H, C on my next 5 tries, whereafter the word PATCH was revealed as the correct target word.
Why would they avoid words like these? It makes it all the more interesting. In your case, instead of guessing BATCH, CATCH, HATCH, etc. one after the other, I‘d recommend to try BEACH, LEMON and WIPED, giving you the right word in fewer tries.
A friend of mine consistently beats me. I went back to the 4 month period Jan-Apr 2023. He had one hole-in-one using the word BROKE on April 22, 2023. He also has 25 games where he gets the answer in 2-0r-less tries. Are these plausible results? Thank you
Hello Rio,
Winning in 2 ties or less 25 times in a row is almost impossible.
Charles
Charles,
The 25 games the he had a 2-or-less were over the four month period, where he played most days, say 110. So, I think it is the binomial distribution.
prob = (110 C 25) x (.065)^25 x (.935)^85 = 2.52517E-08
which is also almost impossible, but much bigger than (.065)^25.
Do you agree?
thanks, rio
Hello Rio,
Yes, I agree. Even with 25 occurrences in 110 games, it is very unlikely.
Charles
I have a friend who posts her NYT Wordle results under mine in Facebook. In 32 days, she has 7 games where she got it in two. But I don’t even know if she played daily, because she doesn’t post her results every day. She’s never posted a losing game. But even if she did play 32 games, that 7 seems impossible to me. She insists that she uses no aids, “just my mind.” It could be that she tries every game to guess it right on the 2nd entry. And when she doesn’t get it, often in that scenario one loses a turn at playing strategically, and possibly doesn’t get it at all. Hence no posted results by her for that game. Have you ever heard of anybody being this successful at getting it in on the 2nd try?
Hi Christine,
Yes, I have heard of people who claimed this much success of getting the word in 2 tries, but I doubt that these claims were valid.
Charles
In our little FB competition, one player has claimed to have gotten five 2s in a row. I am very skeptical of this and my search brought me to this article. The odds of this has to be vanishingly small.
Hello Marilyn,
Yes, the odds are very small. The probability is at best .00000142.
Charles
I play Wordle in a group of 4 people every single day. We share our results. In 424 games played so far my results are:
1: 1
2: 42
3: 118
4: 144
5: 84
6: 30
Failed to get it: 5
Needless to say my whole group, includes my partner, hates me and think I must be cheating. But my partner regularly watches me and confirms I do not cheat.
I will admit some of my 2 guesses are pure luck. Others are strategy.
So getting 2: 25 times is very achievable.
Hello Cherree,
Counting the 5 failed attempts as 7, your average score is 3.89. This is close to 3.69 average for the strategy we describe on the website.
Charles
He was likely playing on a different account earlier in the day lol
I’m new to Wordle so I’ve only played 57 games but I’m happy as long as I work out the 5 letter word within 6 tries (which I have done so far). I do feel chuffed if I get it in two (which I’ve done twice) but actually I enjoy the challenge of having to work it out and feel a bit cheated when I get it right too soon!
My stats are 2×2, 3×18, 4×21, 5×13, 6×3 so I guess I’m pretty average. 🤔😊 It’s interesting to read all the odds though. 👍
Hi Suzie,
It looks like you are doing quite well. In time you will likely reduce the number of 5’s and 6?’s. The most important thing is that you are having fun,
Charles
I’ve always started Wordle with TRACE, which I chose because it’s my name minus the “Y”. Interesting to find out that is the best word statically to start with. What are the chances of that? I’ve had very good luck with this starting word and solve in 3 or less 45% of the time.
Listen, I don’t math very well. I can’t follow all of these statistics you are discussing. I’m going to need you to break this down for me in simple terms.
I play Wordle every day. Still. My strategy is to start with the first 5 letter word that pops into my head. Today marks the 3rd time I’ve guessed the correct word on the 1st try. I don’t usually talk about my stats with people because I get tired of people assuming that I cheat. Why on earth would I bother cheating?? I’d rather just not play than go to the trouble of cheating at a game that has no winner, no loser, is a relatively private and personal game and is a fad that has pretty much ended for everyone in the world. Anyway, is guessing in the first try, 3 different times in the last year and a half, a pretty big deal. Because I kind of feel like it might be. Please tell me. Am I a genius. Have I finally found a talent after living 40 years without being particularly good anything?? Or is it just no big deal?
Hi Sara,
Congratulations. I estimate that there is a 14.6% probability (i.e. about 1 chance out of 7) of guessing the word in one try even once a year. You are very fortunate to do it 3 times.
Charles
Hi Sara,
Today was my 3rd time getting the right word on my first try, and of course without cheating. I generally do the same as you, I put the first word that pops into my head. I have only been playing since April 2022, and my stats show I have played 204 games, though I think I must have played more than that, perhaps on a different device that wasn’t logged in to my account. And second guesses? My stats show 10. I do want to say that 1 of my 3 firsts was FEAST on Thanksgiving which was hardly a stab in the dark but kinda a give away so maybe only 2 of my 3 “count”
Congrats on guessing it right first time more than once. I’ve never done it and have played for a few years. Not meaning to diminish your achievement, but guessing it first time is exactly that, a guess. I think getting it on the 2nd go is harder…
Sara, I’ll add my congratulations as well. There are a total of 12,986 five letter possible guesses and only 2,309 possible solutions.
https://www.wordunscrambler.net/word-list/wordle-word-list
Both these lists are available online. If you guess from the answer list you are, obviously, about 5 times more likely to get it in one try, but many of those words are unproductive first guesses if you miss. So, I am assuming you are using good starter words such as the ones Charles suggests. Thus your probability of solving is about #plays/2309. If you play 500 times in 1.5 years, here is the probability of getting three ones.
prob = (500 C 3) x (1/2309)^3 x (2308/2309)^497 = 0.001356366
This means the odds are about one thousand to one. If there are about 100 thousand people who play every day, then about 136 will have 3 one’s in 1.5 years. You are one of the lucky ones.
Lastly, I should point out that I don’t know if the NYT will pick any common first guesses for the actual answer on any given day. Perhaps Charles might know that.
Once again, congratulations,
rio
There is atheory, not entirely crazed,that says the answer is in the air! Or the collective unconscious. It’s called Morphic Resonance. Best to play later in the day!
Yeah I would say that “theory” IS “entirely crazed” – it’s just nonsense. Sorry to be blunt.
It was suggested in another article that people who guess the correct word in 3 or less Wordle guesses are cheating. Scrabble, and Crossword enthusiasts use a game specific dictionary, and it’s not considered cheating to do so. Why should Wordle be any different from other word games. I proudly use Word Hippo as a guide, not to cheat. Here’s my stats:
3 guesses, 52 wins
4 guesses, 92 wins
6 guesses, 28 wins and that was a year ago when I first started out.
I’ve only lost twice.
Thanks for the probability calculation and patterns. Tonight, I will try Trace as a first word then shamelessly use my Word Hippo.
Hello Coleen,
I am not suggesting that guessing the word in 3 or fewer tries is cheating. I certainly manage to do this about half the time.
The approach described on the website ensures that you will always win within 5 tries starting with TRACE.
Charles
I used to use “tears” but many words end in “e” so I changed to”stare”…. I am way above your probability for second guess wins. As comparable as my word is to your list in chosen letters (actually, both words), you might want to check to see if you overlooked it.
Hi Ben,
“stare” is an excellent choice. The probability of a win within 2 tries is 133/2315, only a little less than the words on the list in Figure 2.
The probability for a win in two for “tears” is 128/2315. There is no chance of a win in 1 try.
You might do better (or worse) than these probabilities. As we all know, given 10 tosses of a fair coin, you should expect to get 5 heads on average (since the probability is 1/2 for a head). You may, in fact, get 7 heads (or 3 heads) or some other number between 0 and 10.
Charles
I also began with “tears” with great luck but changed to “stare” because I want to win with my starter one day. I have gotten it in two 28 times or 7.16%. Love this game!
Hi Charles. Today I solved Wordle in one guess. I cheated. It was revenge guessing and I’m not ashamed in the slightest.
It was one of those words with multiple possible answers, with a one letter difference. By the time I ran through my options, I ran out of lines; and patience. Those kinds of words burn my bottom. So I deleted my browser app, reloaded Wordle and guess what, “genius!”. Thank you. I know. It was nothing. Really.
I have no regrets. It’s a good way to start over fresh and tell Wordle to go f… Oh, wait. That’s a four letter word.
Anyhow, thanks for the info. I’ll try “trace” tomorrow, after I’m done brooding over losing to multiple choice.
#@$*&#!
Translation:
Cheers!
Next time when you encounter one of those words, try words that mostly consist out of the possibilities for the missing letter instead of trying possible solutions one after the other.
So instead of:
HATCH
BATCH
LATCH
MATCH
you guess:
HATCH
BLAME
… so after two tries you have gathered as much information as with the four tries in the first example.
Good advice.
Love your analysis.
I’m fascinated by the probabilities in Wordle but struggle working out odds. In looking at the issue if someone is cheating, I think looking at their first guess is most indicative as this does not use any skill (ignoring remembering the list of past words). So, could you provide the probability for the first word guessed, assuming an optimum strategy, of getting each of zero Greens, 1 Green, 2 Green, 3 Green, 4 Green or 5 Green.
Could you then show how to calculate the combined odds for a sequence, for example – for 5 games a result of zero G, 4G, 2G, 3G and 3G
Alternatively, is it better to look at the odds of hitting a Green with each letter guessed, and then, using the same 5 game example, look at the odds of hitting 12 Green (0+4+2+3+3) from a total of 25 letters guessed?
Hi Dave,
I am not sure what you mean by “the probability for the first word guessed”. Do you mean guessing the target in one guess or something else? No matter which word you use as a first guess, provided it comes from the 2,315-word dictionary, the probability of guessing the target in one guess is 1/2315.
Assuming that you select TRACE, then the probability of 0 G’s is 1336/2315, the probability of 1 G is 714/2315, the probability of 2 G’s is 219/2315, the probability of 3 G’s is 38/2315, the probability of 4 G’s is 7/2315, and the probability of 5 G’s is 1/2315.
Charles
Hi Dave,
You are actually on the right track here, as I’ve been analysing some people who post every day on FB, and the most obvious “tell” is that they get too many letters correct on their first guess! As mentioned on this website, ORATE (or other combinations of those letters) will get the highest possible number of hits (yellow and green) on average over time, but it’s still well below 2 per game. Anyone consistently averaging over 2 hits on their first word is either clairvoyant or getting some “help” from somewhere. Keeping in mind that luck can play a part for a while, you probably need to check at least 50 games, but if you find someone averaging well in excess of 2 hits on their first word, you have a right to be suspicious! In particular, if they claim they choose their starter randomly, they should average a lot less than 2, because they will be using words with much lower average success rates.
If someone is getting a little “help”, it’s very hard not to choose a starter word that has more hits than average, but they won’t realize they are doing this. Whilst there are no doubt some people who know the exact word before they play (there are heaps of ways to find out), I would suggest that most simply use hints gained from seeing FB posts of other players, in particular from players they know that use a known starter word! For example, I know one player who always starts with AUDIO and posts daily from New Zealand, so you can effectively start from Line 2 instead.
Ian, I don’t know if you’re ever going to come back and read this since I am posting this way after your original post, but your analysis sounds very reasonable to me. It’s funny that you mentioned the word ORATE, because, for the longest time, I opened with OATER. I just stumbled on that word on my own, in part after studying letter probabilities. But, the more I have learned the game, the more I have realized that there is more to an efficient start word than that. I have recently switched to TARSE, which I understand has been analyzed to be among the most efficient opening words. I am assuming at least a “second level analysis” was done to look at all the remaining groups after round one, and how easy it is to eliminate among those in the next round, with TARSE and every other word. But nothing I read on this topic explained the analysis and that much detail.
Probably asked before but does Wordle ever repeat the target word? If it doesn’t then chances of arriving at the answer would improve every day (so long as you keep a record of target words).
Hi Clay,
I feel like a knowledge of past wins changes future probabilities of winning. Committing to memory several wins, would raise the probability each day of getting the target in less guesses. For instance, I guessed the target word on the first try back in the spring, and now I will never use that word in my future guesses. This reduces the dictionary list by one. I can do this with several other winning words, also. I am realizing that the probabilities of winning in less tries can also go up for those blessed with great memories. Or those blessed with the ability to archive their winning answer for future reference.
Hi Charles,
I noted somewhere that the average number of guesses to solve is 4. Boy, did I freak out when I guessed the correct word in one guess the second day I played Wordle. Ha! Since then, I’ve guessed the correct word in 4 guesses 60% of the time and never taken more than the 6-guess limit.
I guess I’m ok with ‘average’ 😬.
Hi Clay,
I believe that the average is less than 4 (more like 3.425) if you play properly.
I plan to add an explanation about this shortly.
Charles
I always use the same starting word, MAIRE. And I have a consistent 9-10% rate for guessing the target on the second guess in say over a hundred puzzles. Can being a word nerd beat the odds, or will I die before statistics catch up with me?
Hi Matt,
After the first guess of MAIRE, there are 125 non-empty patterns. This means that the probability of guessing the target word within 2 tries is 125/2315 = 5.4%. Your 9-10% rate is certainly beating the odds. Starting with TRACE would improve your odds to 150/2315 = 6.48%.
Charles
Hmmm…the problem with the reasoning is knowledge of the 2315 limited dictionary of five letter words. Nobody has that, unless you look up the old Wordle source code.
Precepts:
(1) A given player knows a certain finite number of five letter words that potentially qualify (eliminated past tenses, common plurals, etc., which Wordle never seems to use).
(2) The player does not know whether that word is in Wordle’s limited list or not.
(3) Wordle will in fact accept words that are not in its dictionary but which are among the valid English words in an (unknown to me) external dictionary of some sort.
This makes the probabilities nearly impossible to calculate.
If you know the word is in the dictionary, and you use the same word reliably every day, then yes it’s 1/2315. Otherwise it’s a finite but very large number bounded by the number of valid words in the external dictionary that it will accept and count as a guess.
To make things interesting, when I do the puzzle each day, I start with a candidate word from Spelling Bee. I pick whatever word among the Spelling Bee answers has five unique letters, based on which such word I find first while doing Spelling Bee. (If there’s no candidate, I go to the first five letter word with repeating letters. On the rare occasion there are no five letter words in Spelling Bee — this happens — I use a five letter word random picker tool on the web and use the first word it spits out.)
This is an undefined but bounded number of words, but based on the dictionary Spelling Bee uses — which has contained words not in the Wordle dictionary, but which also occasionally disallows words Wordle allows, although this has only happened once as long as I’ve been doing the puzzles together like this.
So I am sitting here trying to calculate the expected number of days before I get a “1” using this method. Perfect knowledge of the 2315 words, and using the same word, and presumably knowledge of past solutions, the probability approaches 1.0 with each passing day. But with my approach, the only bounding condition is what the Spelling Bee editors choose, and it seems like reasonable odds that with a different starter word every day, the probability is measured in terms of millions of years, not 6.3245 years or a median of 3.16245.
Hi Matt,
1. I got the list of the 2315 possible target words from some website several months ago. They must have gotten this from the Wordle website.
Wordle apparently uses targets only from these 2315 words. It allows you to guess words from a larger dictionary of 12,947 words. I got this list from another website. This list includes some very uncommon words, such as BUMPH. If you consult an unabridged dictionary you can probably obtain a list of a similar size, although there are likely to be some differences.
2. If you guess a word at random as your first guess and Wordle accepts it then it will be one of the 12,947 words in their full dictionary. In this case, it will be possible for you to guess the target word in 1 turn only if your guess is also in the smaller 2315-word dictionary. This will reduce your probability of guessing the target word in 1 try to 1/12947.
3. The 1/12947 probability is calculated as follows: 2315/12947 x 1/2315 + (1-2315/12947) x 0 = 1/12947.
4. The limiting factor here is that Wordle won’t let you guess a word that is not in their 12,947-word dictionary.
Charles
Matt – this is exactly what I was thinking, and you said it all perfectly, so I won’t repeat it!
I don’t know of anybody who utilizes the list of 2315 target words in order to make their guesses. In fact, I imagine that most people would consider that to be cheating. One of the charms of Wordle is actually the universal honor code that all players voluntarily follow. The answer is readily available on google every day, but nobody uses that to create a fabricated “winning in one guess” streak. Further, everyone adheres to a strict “no spoiler” code on social media.
I like your technique of obtaining your starter word! We have a group family text chain where we rotate who choses the starter word each day, and then we all start with the same word. This means that my stats are definitely worse than they could be, since I don’t personally select an optimal starter word each day. But it keeps us all connected, and it’s fun to play “together.” And, I prefer a variety of starter words, even if not optimal. My favorite was the day that I chose “CRYPT” as the family starter word, and the answer was “GLYPH,” which was essentially the only valid 2nd guess!
Kristi,
I agree with you. Everyone (and every group) can have fun playing the game their own way.
I have had fun analyzing the game to figure out various strategies for winning, but I also enjoy playing the game without using these strategies to see what happens.
Charles
Hi Charles,
I am curious if you play in HARD mode. I find when I talk to individuals who play that they never knew there was a HARD mode. I am far from being a statistician and I am curious how much your chances increase by playing the EASY mode.
I apologize if you have previously covered this topic.
Rob
Hi Rob,
I believe that HARD mode is what I have called “reduced” or “restricted” on my website. I have analyzed this situation as well. See, for example: https://real-statistics.com/wordle-strategy/winning-wordle-in-three-tries/
Charles
Hi, we play the NY Times Wordle every day in our house, just for fun. We haven’t discussed our strategies for first words!
My daughter and I both chose the exact same first word today completely by accident. Then almost the same second word and then got it in three.
Is it possible to figure out the chances of us choosing the same first word given that it was a completely random event?
Hi Rosie,
If you truly each pick a 5-letter word from the 2,315-word Wordle dictionary at random, then the probability that you will pick the same word is 1/2315, the same as the probability that you will guess the target word in one try. If you pick from the full Wordle dictionary, the probability is 1/12947.
Since you each have some experience playing Wordle, it is likely that each of you will tend to choose your first guess from a smaller range of words, thereby making it more likely that you pick the same word. If one of you likes the word FUZZY and chooses it as your first guess, then perhaps it is less likely that the other will choose the same word. However, if you are drawn to words like LATER, SLATE, TRACE, etc., then perhaps it is more likely you will both choose the same word.
Charles
Hi Charles,
I have solved Wordle puzzles 523, 524 and 525 all in two tries. I think I should buy a lottery ticket. I’m not a genius and I’m guessing that people think I cheat. Not the case and what fun would that be?
Chantelle,
Congratulations! Yes, you should play the lottery. I estimate that even if you use an optimum strategy, you should achieve this result in one out of 3,750 games.
Charles
I have a friend that I suspect is cheating. Knowing the answer ahead of time, their chosen-at-random start word always seems to have enough hits that they can falsify a legitimate sounding claim to have solved it in 2 to 3 plays. Most weeks look like 2-2-3-2-2-3-2. And they never seem to get a 4 or higher. Imaging that.
What’s the probability of a GYYYY pattern as your first play?
Kevin
Hi Kevin,
1. If your friend plays perfectly (without cheating), then the probability of guessing within 3 tries is about 60%. The probability of doing this 7 times is then about 2.8%. This is unlikely but possible. The probability of guessing the target word in 2 tries in one game is about 6.4%.
The probability of 5 twos and 2 threes in 7 games, even if you play perfectly, is approximately 0.0006%, which is quite unlikely. The probability of at least 5 twos and the rest threes in 7 games is only slightly higher.
Even the probability of just getting 5 or more twos in 7 games is very unlikely at 0.002%.
2. The probability of the GYYYY pattern as your first play depends on what your first guess is. If you use TRACE as your first guess the probability is 0%. If you use SLATE as your first guess the probability is 0.043% (1 time out of 2315).
Charles
Charles:
Thank you for taking the time to answer my question. Much appreciated.
Not sure if I can extrapolate a more simple answer. But if the odds of winning in 3 without cheating is 60%, then would it be fair to say that a realistic weekly distribution might be 3+3+3+4+4+4+4 (in any order) with an occasional 2 thrown in once or twice a month?
Additionally, this person says they track all the words every day and that reveals a pattern. Suspect this is BS also. But if final words don’t repeat, by mid-cycle the pool of possible answers would be reduced by ~182 words which seems equivalent to a 10% reduction in possible answers set. If someone does employ this strategy, how much would that help this person over a more casual person who doesn’t track (and easily forgets) previously played final words?
Kevin
Kevin,
1. If they are tracking the words every day, this would help, provided they knew what to do with the information gathered. I don’t think it would radically increase the number of wins in two though.
2. “3+3+3+4+4+4+4 (in any order) with an occasional 2 thrown in once or twice a month” seems reasonable. You will also get an occasional 5 (and worse if you are not careful). If you play an optimal strategy, you probably can replace one of the 4’s by a 3. I plan to explain this on the website shortly.
Charles
Playing with a friend in the golf format. She is currently 11 under through 7 holes and has guessed it in 2 turns for 8 out of the last 28. She is very smart and I don’t consider she’d ever cheat… but we are playing for money :/ What are the probabilities here?
Hi Andrew,
I am not sure what the “11 under through 7 holes” refers to, but the probability of guessing correctly in two tries 8 out of 28 games is 0.000242 if you play perfectly. The probability of guessing in two tries at least 8 times out of 28 is only slightly higher at .000284. Neither of these is very likely.
Charles
Your probability is totally flawed unless you are assuming you have memorised the Wordle solution list. It doesn’t even take into account the nearly 13,000 words Wordle accepts let alone all the 5 letter English words (around 150,000).
Hello Stephen,
Thank you for your comment.
As you have stated, on this webpage I have only taken into account the 2,315 potential target words.
I extend my results to the full list of 12,497 words on the following webpage:
https://www.real-statistics.com/wordle-strategy/best-second-guess-full-wordle-dictionary/
This is referenced in the last paragraph of this webpage. I have just added a link to the above webpage.
My understanding is that while you can use any word from this list as a guess, only words from the shorter list can be the clue (i.e. target) word.
I don’t go past this list since I had understood that Wordle doesn’t accept any other 5-letter words. Is this not so? Can you point me to a 5-letter word that Wordle accepts that is not on this list?
Charles
I just got today’s wordle (10/6/22) on the second try, and only the second letter was green after my first try. I realize after reading these comments, that that’s not all that great, but I was shocked!
Hi Jessie,
It seems like an excellent result to me.
Some of the comments that you have seen represent more wins in two tries than seems probable. The people who sent thsee comment suspect that the person who achieved such good results is exaggerating.
Charles
10 consecutive days to get 5 eagles and 5 birds – what’s the probability to achieve that? I find it so hard to believe.
Hello Currie,
Assuming that an eagle is a win in 2 tries and a bird is a win in 3 tries, the probability is roughly 1 in 100,000.
Charles
Yes that’s what I meant. Thank you for your answer!
The Wordle is tearing families apart!! I’ve been doing the wordle in competition with my sister since May 2022, using watsapp. She’s not an especially sharp-minded person (e.g. she still hasn’t worked out that the wordle doesn’t use four-letter nouns or verbs with an S on the end), but has somehow managed to get it in two guesses more than once a week (I counted them: 23 times in 19 weeks). As much as I want to believe she wouldn’t cheat at a game, the odds of this are too great. Would you believe it?
The probability of winning in two guesses 2 or more times in 7 days is about 7% assuming optimum strategy. The probability of winning in two guesses 23 or more times in 7*19 games is at best 0.00138%.
Charles
If I am in a Wordle competition that runs for 18 days, and I can see everyone else’s (apparent) results, how do I calculate the probability that they actually achieved this?
It depends on what you mean by “they actually achieved this”. E.g. suppose you were in a competition to see who would get the most heads in 20 tosses of a coin. Now suppose the other player got 15 heads. Actually, the probability of this is 1.5%. This means that the event is rare but quite possible. Now suppose, you played against 2 other players and they both got 15 or more heads. The probability of this is 0.0035%, which is quite unlikely. The “devil is in the details”. It depends on your expectations and the actual results.
Charles
I just want to assess one individual’s results. Say for example over 18 days someone’s Wordle results are the below, what is the probability of this occurring without cheating?
4 2 3 3 4 3 2 4 3 2 4 4 3 2 3 3 3
It seems to be possible, but very unlikely. Even using the best strategy, the probability of a win in 2 guesses is 6.4%. The probability of guessing in two tries 4 times out of 17 tries is then 1.7%. The probability of guessing in two tries at least 4 times out of 17 tries is about 2.1%. I would guess that a result at least as good as the one you reported is much less than 1%.
Charles
What’s the possibility of getting it in two guesses 8 days out of 9? Trying to call out a cheater here…
Hi Colleen,
The probability of getting the target word in exactly 2 guesses 8 days out of 9 is extremely low. Assuming that the person uses the best strategy as explained on this webpage, the probability is 0.000000448%. This is calculated in Excel by =BINOM.DIST(8,9,149/2315,FALSE).
Charles
I guessed the word not once but twice and it seriously spooked me. I dont keep a record of past words, the words were loser and voice. If only I could forsee the lotto numbers ho hum.
What’s the probability on getting today’s wordle 24.08 having only got the third letter in opening guess ie. xxAxx
Hi Neil,
Assuming that your initial guess was “slate”, there are 48 words in the dictionary with the pattern xxAxx. Thus the probability of this happening is 48/2315 = 2.0734%. If your goal is to win within 3 turns, I suggest that you use “churn” as your second guess.
Charles
In today’s wordle 19.08.2022 , I entered three guesses for my first three attempts and there were no correct letters. What are the mathematical odds of this unfortunate event? I.e. 3 turns no correct letters.
Hello Stephen,
The odds of this happening depends on what three guesses you made. E.g. if your three guesses are fizzy, pygmy, piggy, then the odds are quite high. Of course, these are not likely to be your guesses. Now suppose you choose slate as your first guess (my recommendation) and you find no matches. You next choose round as your second guess (my recommendation in this case) and again you find no matches. If you choose wimpy as your third guess, then there is no chance that you will find no matches (since you have used all the vowels).
Charles
If you exclude past words as possible answers, slate has a 0.0742 chance of leading to a guess in two. That’s accounting for 416 past words.
Hi Nathan,
How did you calculate 416? Also, how does 416 result in a 0.0742 chance of winning in two guesses?
Charles
I’m not sure the first paragraph is quite correct in its assertion that every guess has probability of 1/2315. Firstly, there are many more 5-letter words from which the 2315 have been selected. If you know what these are, and NYT select randomly from them so that any particular word can be reselected and therefore for instance it is possible that the same word could be used on consecutive days, then it would be 1/2315. Otherwise every word would not have probability of 1/2315.
Hi John,
Yes, you are right, but, as usual, simplifying assumptions can be useful. The 1/2315 value is reasonable provided (1) you know the 2315 word dictionary and only select words from this dictionary and (2) NYT randomly selects words from this dictionary (and if they don’t repeat selections then you haven’t been keeping track of previously selected words).
Charles